Question: $ C = \left[\begin{array}{rr}2 & 2 \\ 0 & 4 \\ -2 & 2\end{array}\right]$ $ B = \left[\begin{array}{r}2 \\ 0 \\ 4\end{array}\right]$ Is $ C B$ defined?
In order for multiplication of two matrices to be defined, the two inner dimensions must be equal. If the two matrices have dimensions $( m \times  n)$ and $( p \times q)$ , then $ n$ (number of columns in the first matrix) must equal $ p$ (number of rows in the second matrix) for their product to be defined. How many columns does the first matrix, $ C$ , have? How many rows does the second matrix, $ B$ , have? Since $ C$ has a different number of columns (2) than $ B$ has rows (3), $ C B$ is not defined.